Is it okay If I put a smaller filter in there temporarily because the one filter that does fit is super dirty and I have yet to go to the store for a new one

You can use a smaller filter but also clean the old one and use it in conjunction with the other temporarily. Get to the store as soon as you can as you could kill your fish if you don't.

I'm guessing you mean one of those like filter floss type cartridges? Just rinsing out the old one is a better option. The cartridge really shouldn't be changed until rinsing it ends with it falling apart. Just rinse it out in tank water in a separate container. Rinsing it in tap water will kill much of the bacteria growing in it.

005: Maintaining Your Freshwater Aquarium Setup - Aquarium Setup